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Neural networks storing multiple discrete attractors are canonical models of biological memory. Previously, the dynamical stability of such networks could only be guaranteed under highly restrictive conditions. Here, we derive a theory of…
In this paper we will investigate dynamic stability of percolation for the stochastic Ising model and the contact process. We also introduce the notion of downward and upward $\epsilon$-movability which will be a key tool for our analysis.
The dynamic stability of the Boolean networks representing a model for the gene transcriptional regulation (Kauffman model) is studied by calculating analytically and numerically the Hamming distance between two evolving configurations.…
Inspired by strict-monotonicity criteria for the time constant in first passage percolation, we investigate convex ordering of point processes in relation to the time constant in first contact percolation. In a nutshell, first contact…
We study the stable attractors of a class of continuous dynamical systems that may be idealized as networks of Boolean elements, with the goal of determining which Boolean attractors, if any, are good approximations of the attractors of…
Planar wave trains are traveling wave solutions whose wave profiles are periodic in one spatial direction and constant in the transverse direction. In this paper, we investigate the stability of planar wave trains in reaction-diffusion…
The problem of online change point detection is to detect abrupt changes in properties of time series, ideally as soon as possible after those changes occur. Existing work on online change point detection either assumes i.i.d data, focuses…
We consider a family of percolation models in which geometry and connectivity are defined by two independent random processes. Such models merge characteristics of discrete and continuous percolation. We develop an algorithm allowing…
Localized perturbations in a real-world network have the potential to trigger cascade failures at the whole system level, hindering its operations and functions. Standard approaches analytically tackling this problem are mostly based either…
We study the dynamics of solutions of infinitely thin needles up to densities deep in the semidilute regime by Brownian dynamics simulations. For high densities, these solutions become strongly entangled and the motion of a needle is…
We study the Bayesian problems of detecting a change in the drift rate of an observable diffusion process with linear and exponential penalty costs for a detection delay. The optimal times of alarms are found as the first times at which the…
This paper is concerned with the estimation of time-varying networks for high-dimensional nonstationary time series. Two types of dynamic behaviors are considered: structural breaks (i.e., abrupt change points) and smooth changes. To…
Rapid detection of spatial events that propagate across a sensor network is of wide interest in many modern applications. In particular, in communications, radar, IoT, environmental monitoring, and biosurveillance, we may observe…
We study an open discrete-time queueing network that models the collection of data in a multi-hop sensor network. We assume data is generated at the sensor nodes as a discrete-time Bernoulli process. All nodes in the network maintain a…
We investigate the behavior of ultracold bosons in optical lattices with a disorder potential generated via a secondary species frozen in random configurations. The statistics of disorder is associated with the physical state in which the…
In random access protocols, the service rate depends on the number of stations with a packet buffered for transmission. We demonstrate via numerical analysis that this state-dependent rate along with the consideration of Poisson traffic and…
Dynamic networks are interconnected dynamic systems with measured node signals and dynamic modules reflecting the links between the nodes. We address the problem of \red{identifying a dynamic network with known topology, on the basis of…
We introduce and study a new model of interacting neural networks, incorporating the spatial dimension (e.g. position of neurons across the cortex) and some learning processes. The dynamic of each neural network is described via the elapsed…
This study employs scientific machine learning to identify transient time series of dynamical systems near a fold bifurcation of periodic solutions. The unique aspect of this work is that a convolutional neural network (CNN) is trained with…
Static wireless networks are by now quite well understood mathematically through the random geometric graph model. By contrast, there are relatively few rigorous results on the practically important case of mobile networks, in which the…